cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 15 results. Next

A155841 Primes of the form q*p+2^p where p is prime, q=3.

Original entry on oeis.org

17, 47, 149, 2081, 8231, 140737488355469, 300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087678029
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Crossrefs

Cf. A057664

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=3*p+2^p],AppendTo[lst,p]],{n,5!}];lst

A057678 Primes of the form 2^p - p where p is prime.

Original entry on oeis.org

2, 5, 8179, 524269
Offset: 1

Views

Author

Labos Elemer, Oct 19 2000

Keywords

Comments

Next term, if it exists, has more than 618 digits. - Emeric Deutsch, Mar 27 2005
Next term, if it exists, has more than 10,000 digits.
The corresponding primes p are: 2, 3, 13, 19, .... - Gerasimov Sergey, Jul 26 2013
The corresponding 2^p - 1 are 3, 7, 8191, 524287 which are Mersenne primes (A000668). Is this the case for all members of the sequence? None of the other Mersenne primes < 2^132049-1 correspond to members of the sequence. - Robert Israel, Jul 18 2016
Next term is 2^481801-481801. 2^481801-1 is not a Mersenne prime. - Joerg Arndt, Jul 19 2016

Examples

			p=3 is prime, and so is 2^p - p = 8 - 3 = 5, so 5 is in the sequence. - _Michael B. Porter_, Jul 19 2016

Crossrefs

Cf. A000668, A057663, A057664, A057665, A056677.

Programs

  • Maple
    a:=proc(n) if isprime(2^ithprime(n)-ithprime(n))=true then 2^ithprime(n)-ithprime(n) else fi end: seq(a(n),n=1..310); # Emeric Deutsch
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[Table[2^p-p,{p,Prime[Range[20]]}],PrimeQ] (* Harvey P. Dale, Sep 20 2018 *)

A129962 Primes of the form 2^k + k.

Original entry on oeis.org

3, 11, 37, 521, 32783, 549755813927, 37778931862957161709643, 2417851639229258349412433, 618970019642690137449562201, 266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867389
Offset: 1

Views

Author

Cino Hilliard, Jun 10 2007

Keywords

Comments

It is convenient, although not necessary, to let k be an odd number since k even => 2^k + k is even > 2.
Conjecture: sequence is infinite.
If k is prime we have A057664.

Examples

			For k = 3, 2^3 + 3 = 11 prime, so 11 is a term.

Links

Crossrefs

Cf. A052007 (values of k), A057664, A081296.

Programs

  • Magma
    [a: n in [0..400] | IsPrime(a) where a is 2^n + n]; // Vincenzo Librandi, Jul 25 2019
  • Mathematica
    Select[Table[2^n+n,{n,600}],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)
  • PARI
    f(n) = forstep(x=1,n,2,y=2^x+x;if(isprime(y),print1(y",")))

A155842 Primes of the form q*p+2^p where p is prime, q=5.

Original entry on oeis.org

23, 163, 137438953657, 2305843009213694257, 862718293348820473429344482784628181556388621521298319395315527976057, 19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611325257
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Comments

The next term has 4702 digits. - Harvey P. Dale, Nov 02 2024

Crossrefs

Cf. A057664, A155841

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=5*p+2^p],AppendTo[lst,p]],{n,5!}];lst
Select[Table[5p+2^p,{p,Prime[Range[100]]}],PrimeQ] (* Harvey P. Dale, Nov 02 2024 *)

A155843 Primes of the form q*p+2^p where p is prime, q=9.

Original entry on oeis.org

191, 536871173, 2199023255921, 10384593717069655257060992658441209
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Crossrefs

Cf. A057664, A155841, A155842

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=9*p+2^p],AppendTo[lst,p]],{n,5!}];lst

A057663 Primes p such that p + 2^p is also a prime.

Original entry on oeis.org

3, 5, 89, 317, 701
Offset: 1

Views

Author

Labos Elemer, Oct 16 2000

Keywords

Comments

Different from A056206, where, e.g., at n=89, 89 is not minimal, A056206(89)=29 and not 89.
a(6) > 27479. - Ralf Stephan, Oct 23 2002
Intersection of A000040 and A052007. - Iain Fox, Nov 08 2017
a(6) > 678561. - Iain Fox, Nov 08 2017
Every term other than 3 is congruent to 5 (mod 6). - Arkadiusz Wesolowski, Nov 14 2017
These terms satisfy phi(k + 2^k) = phi(k) + 2^k, where phi is A000010, the Euler totient function. Conjecture: this sequence gives all numbers k that satisfy the condition phi(k + 2^k) = phi(k) + 2^k. - Juri-Stepan Gerasimov, May 23 2019

Examples

			q=3, 2^3 + 3 = 11 a prime.

Crossrefs

Cf. A000010, A006127, A056206, A056208, A057664, A057665.

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | IsPrime(2^p+p) ] // Vincenzo Librandi, Aug 07 2010
  • Mathematica
    Select[Prime@ Range[10^3], PrimeQ[# + 2^#] &] (* Michael De Vlieger, Nov 08 2017 *)
  • PARI
    lista(nn) = forprime(p=3, nn, if(ispseudoprime(p + 2^p), print1(p, ", "))) \\ Iain Fox, Nov 13 2017
  • Sage
    [n for n in (1..1000) if is_prime(n) and is_prime(2^n+n)] # G. C. Greubel, May 24 2019

A155844 Primes of the form q*p+2^p where p is prime, q=13.

Original entry on oeis.org

47, 97, 131293, 140737488355939, 2361183241434822607771
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Crossrefs

Cf. A057664, A155841, A155842, A155843

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=13*p+2^p],AppendTo[lst,p]],{n,5!}];lst

A155845 Primes of the form 2^p-p*q where p is prime,q=3.

Original entry on oeis.org

-2, 17, 107, 524231, 8388539, 162259276829213363391578010287807
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Comments

The next term has 1342 digits. - Harvey P. Dale, Dec 09 2013

Crossrefs

Cf. A057664, A155841, A155842, A155843, A155844, A057678

Programs

  • Mathematica
    q=3;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
Select[2^#-3#&/@Prime[Range[900]],PrimeQ] (* Harvey P. Dale, Dec 09 2013 *)

A057665 Numbers k such that prime(k) + 2^prime(k) is prime.

Original entry on oeis.org

2, 3, 24, 66, 126
Offset: 1

Views

Author

Labos Elemer, Oct 16 2000

Keywords

Comments

a(6) > 3002, since prime(3002) = 27479 (see comment by Ralf Stephan in A057663). - Michel Marcus, Dec 20 2013
These values correspond to indices ip = 2, 3, 9, 10, 11 where A052007(ip) is prime. - Michel Marcus, Dec 20 2013
If it exists, a(6) > 15*10^3. - Michal Paulovic, Sep 24 2023
If it exists, a(6) > 30*10^3. - Michael S. Branicky, Sep 01 2024

Crossrefs

Cf. A052007, A057663, A057664.

Programs

  • Mathematica
    Select[Range[10^3], PrimeQ[# + 2^#] &@ Prime@ # &] (* Michael De Vlieger, Oct 26 2017 *)
  • PARI
    isok(n) = isprime(prime(n) + 2^prime(n)); \\ Michel Marcus, Dec 19 2013

Formula

a(n) = primepi(A057663(n)). - Michel Marcus, Dec 20 2013

Extensions

Name edited by Michel Marcus, Dec 19 2013

A155846 Primes of the form 2^p-p*q where p is prime,q=5.

Original entry on oeis.org

-7, 7, 1993, 130987, 536870767, 9007199254740727
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 28 2009

Keywords

Crossrefs

Cf. A057664, A155841, A155842, A155843, A155844, A057678, A155845

Programs

  • Mathematica
    q=5;lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p*q],AppendTo[lst,p]],{n,5!}];lst
Select[Table[2^p-5p,{p,Prime[Range[50]]}],PrimeQ] (* Harvey P. Dale, Jul 02 2018 *)
Showing 1-10 of 15 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.